PvP means you can be attacked anytime (ie = ganked, normally) in all level 20+ zones. Most PvP occurs in Battlegrounds though, where you and a small group of other players join up to fight a group from the opposite faction.
PvE realms on the other hand, you need to enable PvP before someone can attack you out and about. They also have Battlegrounds so you can still PvP but without the hassle of being attacked when you're trying to do something else.
Personally Battlegrounds killed PvP in my opinion as before on PvP realms there was active world PvP (where pitched battles were fought) and it lived up to the name World of Warcraft.
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